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causal edges assumption, endows directed paths with the unique role of carrying causation along them. Additionally, causal edges assumption is asymmetric; β π is a cause of π β is not the same as saying β π is a cause of π .β

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Exchangeability means that the treatment groups are exchangeable in the sense that if they were swapped, the new treatment group would observe the same outcomes as the old treatment group

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hat provide the link between two tables β in Table A has to match the corresponding items in Table B (if a relation is one-to-many). A possible solution to this problem is to synthesise data at <span>multiple granularity levels: 1. Use unsupervised machine learning to cluster data at parent level (customer). 2. Synthesise this table, including the cluster identifier. 3. Randomly assign a syn

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hat much of the work for causal graphical models was done in the field of probabilistic graphical models. Probabilistic graphical models are statistical models while causal graphical models are <span>causal models. <span>

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paths with the unique role of carrying causation along them. Additionally, this assumption is asymmetric; β π is a cause of π β is not the same as saying β π is a cause of π .β This means that <span>there is an important difference between association and causation: association is symmetric, whereas causation is asymmetric <span>

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are associated or not associated. Another way of saying this is whether two nodes are (statistically) dependent or (statistically) independent. Additionally, we will study whether two nodes are <span>conditionally independent or not. <span>

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The flow of association is symmetric

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In generating synthesised data, normally we use the finest granularity. For instance, order_id would represent a store managing orders, or person_id could represent a population. However, when we have multiple tables linked by foreign keys, then different levels of granularity emerge and the concept of finest granularity becomes ambiguous

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To get this guaranteed dependence between adjacent nodes, we will generally assume a slightly stronger assumption than the local Markov assumption: minimality

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Flow of Causation The flow of association is symmetric, whereas the flow of causation is not. Under the causal edges assumption (Assumption 3.3), causation only flows in a single direction. Causation only flows along directed paths. Association flows along any path that does not contain an immorality

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The potential outcome that is observed is sometimes referred to as a factual. Note that there are no counterfactuals or factuals until the outcome is observed. Before that, there are only potential outcomes

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In contrast, the non-strict causal edges assumption would allow for some parents to not be causes of their children. It would just assume that children are not causes of their parents. This allows us to draw graphs with extra edges to make fewer assumptions, just like we would in Bayesian networks, where more edges means fewer independence assumption

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there is no reason to expect that the groups are the same in all relevant variables other than the treatment. However, if we control for relevant variables by conditioning, then maybe the subgroups will be exchangeable. We will clarify what the βrelevant variablesβ are in Chapter 3,

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consistency encompasses the assumption that is sometimes referred to as βno multiple versions of treatment.β

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Other (wrong definitions of confounder): - change in estimate definition - conventional definition

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amples. In the first causal graph here you see that A and Y have no common causes. And therefore, any association between them will be causation. This is the setting that we expect to find in a <span>randomized experiment. <span>

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Systematic bias is an association between the treatment A and the outcome Y that does not arise from the causal effect of A on Y.

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In the second graph here, you see that A and Y have a common cause, L. But there is no causal effect of A on Y. In this setting, all the association between A and Y is due to confounding.

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